Optimization Theory with Applications (Dover Books on Mathematics) by Donald A. Pierre (PDF)

Description

Optimization principles are of undisputed importance in modern design and system operation. They can be used for many purposes: optimal design of systems, optimal operation of systems, determination of performance limitations of systems, or simply the solution of sets of equations. While most books on optimization are limited to essentially one approach, this volume offers a broad spectrum of approaches, with emphasis on basic techniques from both classical and modern work.After an introductory chapter introducing those system concepts that prevail throughout optimization problems of all types, the author discusses the classical theory of minima and maxima (Chapter 2). In Chapter 3, necessary and sufficient conditions for relative extrema of functionals are developed from the viewpoint of the Euler-Lagrange formalism of the calculus of variations. Chapter 4 is restricted to linear time-invariant systems for which significant results can be obtained via transform methods with a minimum of computational difficulty. In Chapter 5, emphasis is placed on applied problems which can be converted to a standard problem form for linear programming solutions, with the fundamentals of convex sets and simplex technique for solution given detailed attention. Chapter 6 examines search techniques and nonlinear programming. Chapter 7 covers Bellman’s principle of optimality, and finally, Chapter 8 gives valuable insight into the maximum principle extension of the classical calculus of variations.Designed for use in a first course in optimization for advanced undergraduates, graduate students, practicing engineers, and systems designers, this carefully written text is accessible to anyone with a background in basic differential equation theory and matrix operations. To help students grasp the material, the book contains many detailed examples and problems, and also includes reference sections for additional reading.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have not seen a book in my life so poorly written. This is no way a student-friendly book. It has no explicit explanations whatsoever. It seems the problems at the end of each chapter are taken from another book. Have to live with that for a whole semester. Cannot get why our professor chose this book for his class when there are plenty of well-written up-to-date books.

⭐My gf needed this for her phd qualifying exam.It got her well prepared for it apparently, as she passed it!

⭐Most of the topics in this book still seem important, but unfortunately, for each topic,there is a more clear and modern treatment that has been since provided in another book.For an introduction to the calculus of variations, try Weinstock’s book.Also, “Algorithms” by Cormer, Leiserson, Rivest, and Stein has good chapters on the simplex algorithmand dynamic programming (from a discrete perspective). And Nocedal and Wright have written aan excellent survey of numerical optimization.

⭐Dover lists this book as being published in 1989. However, it was actually published in 1969. Due to the rapid progress in this field over the last 40 years, the book consequently very much out-of-date. However, it may be of interest to those who want a historical context for the evolution of the technology to current methods. Acceptable buy for five dollars.

⭐The author is very unclear in the conclusions he makes and in how he arrives at certain very important equations. Many proofs are “left to the reader” which proved to be frustrating as I was using the book to learn calculus of variations for the first time. I would greatly discourage using it as a text to introduce yourself to optimality.

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